On lifting perfect codes
| Autor: | Rifà, Josep, Zinoviev, Victor |
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| Rok vydání: | 2010 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we consider completely regular codes, obtained from perfect (Hamming) codes by lifting the ground field. More exactly, for a given perfect code C of length n=(q^m-1)/(q-1) over F_q with a parity check matrix H_m, we define a new code C_{(m,r)} of length n over F_{q^r}, r > 1, with this parity check matrix H_m. The resulting code C_{(m,r)} is completely regular with covering radius R = min{r,m}. We compute the intersection numbers of such codes and, finally, we prove that Hamming codes are the only codes that, after lifting the ground field, result in completely regular codes. Comment: Submitted to IEEE Transactions on Information Theory |
| Databáze: | arXiv |
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